You’re not actually taking responsibility for him at all if you sack him for minor things which breach your personal values – that’s more like victimising him than taking responsibility for it yourself.
Taking responsibility would be treating him like an adult and having a face to face chat with him about all the issues and giving him right to reply – and listening to it properly, without judgement and without prejudice. And I mean listen – say absolutely nothing whilst he talks…
Show him some leadership and you may find him an awesome employee. Sack him and you teach him that managers will use their power irresponsibly, which will become his long term problem he’s likely to carry around for years and hold his career back.
I’m afraid it shows that you lack management experience but I’ll give you this – you’ve thought enough about it to come on here and engage with those who’ve criticised you for your approach. That suggests you are actually thinking about the negative consequences for this lad of your actions – do more of that before you sack him please.
Oh, and have a word with your employer about giving you some management training. I’ve seen so many weak managers over the years wreck people’s work lives because the manager was given line management responsibility without any training… so please make this your employer’s responsibility to support you too.
Good luck… I’m sure this isn’t pleasant